Steps involved in the development and execution of a figure composition in oils

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STEPS INVOLVED IN THE DEVELOPMENT AND EXECUTION OF A FIGURE COMPOSITION IN OILS

A Thesis Presented to the Faculty of the Department of Fine Arts The University of Southern California

In Partial Fulfillment of the Requirements for the Degree Master of Fine Arts

fey

Elton M. Davies January 1950

UMI Number: EP57876

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This thesis, w ritte n by Elton M. Davies under the guidance of h.l.?.... F a c u lty Com m ittee, and app ro ved by a l l its members, has been presented to and accepted by the C o uncil on G ra duate S tudy and Research in p a r t ia l f u l f i l l ­ ment o f the requirements f o r the degree of Master of Fine Arts

n„„ January

Faculty Committee

1950

TABLE OF CONTENTS CHAPTER I.

PAGE

BASIS FOR THE COMPOSITION.............

1

The p r o b l e m ........................ The purpose of this s t u d y .........

1

The subject of the c o m p o s i t i o n ...

1

The value of this s t u d y ...........

1

Discussion of terms .....................

1

Composition ...........................

1

Organization II.

1

...........................

2

PRELIMINARY EXPLORATION ....................

4

First clay model and first working s k e t c h ...............

4

Studies prompted by first sketch . . . .

4

Synthesis of studies and why unsatis­ factory .............................

5

...........................

6

Conclusion III.

THE COMPOSITION AS FORMS IN S P A C E ..... Analysis of compositions essentials

10 . .

10

New working sketch and why satisfactory .

10

Description of resulting threedimensional composition......... Studies prompted by new composition . . .

11 12

iii CHAPTER

PAGE Synthesis into first large drawing . . .

13

Major problems emerging in large

IV.

d r a w i n g ...........................

13

Conclusion...........................

16

THE COMPOSITION AS LIGHT AND S H A D E ........

21

First light-and-shade study, and why unsatisfactory ......................

21

Second clay model, and resulting satis­ factory light-and-shade study

....

Application of study to large drawing Weaknesses revealed and rectified

21 .

...

22

Conclusion........................... V.

THE COMPOSITION AS TWO-DIMENSIONAL DESIGN

22

23 .

Design considerations so f a r ..........

27 27

Reasons for making design problem g e o m e t r i c a l ........................

27

........

28

Summary of resulting problems

Choice of mean proportion as basis for organizing design

..................

28

First application, and why unsatis­ factory

...........................

30

Discoveries resulting from failure . . .

30

Two new points of d e p a r t u r e ..........

31

CHAPTER

PAGE Second and more successful application .

33

Results derived from application . . . .

34

Advantages of geometric approach to this composition's pattern ..........

VI. VII.

37

Conclusion...........................

38

THE COMPOSITION AS AIDED BY DISTORTION . . .

41

THE COMPOSITION AS COLOR AND AS AIDED BY MANNER OF T R E A T M E N T ....................

A3

Color s k e t c h ..........................

43

Choice of p a l e t t e ....................

43

Distribution of warm and cool tones

43

. .

First manner of painting final canvas,, and why unsatisfactory..............

45

Conclusion...........................

46

BIBLIOGRAPHY...................................

49

A PPENDIX.......................................

52

LIST OP ILLUSTRATIONS ILLUSTRATION

PAGE

1.....................................

7

2.....................................

7

3

8

4 .....................................

8

5.....................................

9

6

9 7.....................................

17

8

17

9

18

10 .....................................

19

11 .....................................

19

12

20

13

20

1A.....................................

24

15 .....................................

25

16 ........................................

25

17

26

18

26

19 .....................................

35

20

39

21

...................................

^0

vi ILLUSTRATION

PAGE

22 ................................

kj

23 .....................................

48

CHAPTER I BASIS FOR THE COMPOSITION I.

THE PROBLEM

The purpose of this study was, (l) to complete success­ fully in oils a composition whose essential features will be described in the next paragraph; (2) to show the steps in its development. The subject of the composition was inspired by an incident which the student glimpsed a long time ago, the memory of which still moves him.

Two Mexican women, well

advanced in age, and possibly sisters, were meeting on the steps of a little house.

Something in their manner suggested

that they had been separated for years, and were now reunited by love and the memory of past sorrow.

A fitting title for

such a subject was considered to be "Return”. The value of this study depends entirely on the degree to which others elect to draw upon it in developing their own methods of composing.

II. Composition.

DISCUSSION OF TERMS In the course of completing the painting

2

the following working definition was tentatively developed: jt. P^-c' Gor^al composition is a piece of research in spatial

organization, the results being stated in terms of two di­ mensions, in such a manner that the arrangement of form and color, consistently treated, merits thoughtful attention through its own intrinsic qualities. In the rare cases where a word is used out of its accepted meaning, authority for the usage is cited in a footnote. Mr. Francis de Erdely, who oversaw the development and painting of the composition, is designated throughout the thesis as the advisor. The writer refers to himself as the student.

III.

ORGANIZATION

The following account is, in one respect, a record of the development of a first composition.

In another, it

is a discussion of the practical application of the under­ lined definition above.

To clarify the application, problems

are isolated by chapters, though scarcely at the expense of chronological order. The preliminary exploration is first described, (Chapter II), then the emergence from this of the composition

3 as forms in space (Chapter III) . Next (Chapter IV) the problem of the light and shade on these forms is treated; then (Chapter V) the placement of the composition on the picture plane; and next (Chapter VI) some of the distortions attending this placement.

Last of all (Chapter VII) the use

of color is discussed, and the manner of handling the paint.

CHAPTER II PRELIMINARY EXPLORATION First clay model and first working sketch. The initial problem was to create,, through imagination, reasoned analysis, and experiment, a living pictorial reality from a hazy, evanescent memory. Several preliminary sketches immediately presented so many problems, chiefly in the spatial relations between the two women, and between these and the porch, that the only solution was to attack them in three dimensions.

Small

plsticine figures, and the elements of a porch (steps, posts, wall, roof) were therefore constructed, and several studies made from these, one of which (Illustration 1) is reproduced. The experience gained from studying the model now enabled the making of the first sketch of a possible future painting (Illustration 2).

This was the first to seem satis­

factory as an actual starting point for operations. Studies prompted by first sketch. The next step was to develop and test it, in terms of objective reality, more seriously than had been possible so far.

A professional

model was therefore engaged, and careful studies (Illustra­ tions 3 and 4) were made of her as nearly as possible in the

5 position of both women in the sketch.

A house was dis­

covered meeting the general requirements of that in the sketch, and a detailed study made of its porch (Illustra­ tion 5 ) • This study, at first made in black and white, was later repeated in color. Synthesis of studies and why unsatisfactory. These materials having been gathered, a series of drawings were made attempting to synthesise them into a composition like the sketch which had inspired them.

Of these drawings the

final one is reproduced as Illustration 6.

A treatment of

the porch as a problem in three-point linear perspective (not illustrated) also went into this drawing. Before its completion, the impossibility of developing a composition from it had become manifest.

The apex to which

the figures converge lies in the same general direction as that to which the porch posts also converge.

The empty spaces

around the figures, especially the upper right and lower left, could be saved from dullness only by filling them with some extraneous decoration, such as may be seen introduced in Illustration 6.

Careful studies for the vine and tree trunk

were actually completed before the conviction was reached that these elements could never become an organic part of the composition.

6 Conclusion.

There remained two courses to follow:

Either to distort the figures so that they filled the space, or to attack the composition afresh.

Since the student

felt as yet unprepared to do the former, the latter was the logical alternative.

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CHAPTER V

THE COMPOSITION AS TWO-DIMENSIONAL DESIGN Design considerations so far. While the discussion s far has been centered on the three-dimensional aspects of the composition, the fact that it was also two-dimensional, and therefore a problem in two-dimensional design, was at no time ignored.

In its simplest form this recognition of

the design aspect consisted in making no single study with­ out pondering the two questions:

(l) Is the rectangle of

the right proportions for this grouping, and (2) is the grouping placed satisfactorily within it? Reasons for making design problem geometrical. Con­ sideration of the two-dimensional problem need not have pro gressed beyond this point.

It so happened, however, that

the geometrical aspects of design had long interested me. I was as much desirous of investigating the use of these aspects, as I was in determining the nature of their abuse, in composition. In one sense there seem to be two schools of opinion on the role of two-dimensional design in composition, one holding that the divisions of the picture plane are best determined by the test of visual satisfaction alone, the

28 other that these divisions are best determined mathematically. Outstandingly successful painting can be produced as evidence of both opinions, for example, Cezanne’s of the former, Rafael’s of the latter.-*-

Consequently a debate on which is

the correct one is fruitless.

The question is, simply, which

can a given painter use most profitably? The student believed that more could be gained from exploring the possibilities of the mathematical approach, than through ignoring it, since it could always be discarded if it proved an encumbrance.

More than this, he had long

been deeply interested in the works of certain painters, notably Piero della Francesca, known to be a mathematician. Summary of resulting problems. This decision having been reached, two questions presented themselves:

First,

what should be the mathematical basis for the design? Second, how could it be used to assist, rather than con­ flict with the three-dimensional aspect of the composition? Choice of mean pro portion as basis for organizing design.

In answer to the first, the student decided, after

some study and experiment, to divide all four sides in mean

1 See M0ssel, Vom Geheimnis der Form und der Urform des Seins, pp. 386-370 for an exposition of Rafael’s use of Geometry in composition.

29 and extreme pooportion,2 and to use the lines connecting these division points as the main divisions of the picture plane.

He was guided to this decision by the following con­

siderations : 1. The mean proportion pleased him esthetically as a basis for the design. 2. It has certain clear connections with both plant and animal structure and the phenomena of g r o w t h . 3 3. It has been used successfully in a wide variety of outstandingly beautiful works of architecture, sculpture, and painting, from ancient times to the present,^ the paintings of Seurat being among the more recent applications of it.5 4. It admits of a simplicity and flexibility in use which other mathematical divisions do not.

2 See any standard text on Plane Geometry. 3 See Ghyka, The Geometry of Art and Life, Chapter VI, for a summary of these connections. Those interested in a more detailed discussion are referred to Thompson, On Growth and Form, especially Chapter XIV, On Phyllotaxis. ^ See MSssel, op. cit. This work can best be described as an historical study of the uses of mathematics in compo­ sition. It is at once more comprehensive and less naive than Jay Hambidge’s work in the same direction. 5 See Ghyka, op. cit., p. 156, for a reference to Andre Lhote's confirmation of this statement.

First application, and why unsatisfactory.

The method

of application was another matter and a more difficult one. The first and most obvious consideration was that since a composition is above all else a study of three dimensions, and since the two-dimensional pattern is subordinate to this, any a pPioPi division of the picture plane merely hampers the unfolding of that composition.

It was clear from the first

day of working that the continual traveling in thought, back and forth between problems of placement in space and those of placement on the picture plane could be fruitful only if kept completely free and open to change, and that the intro­ duction of even one mathematically fixed line was fatal to this freedom. picture.

This was true even of the proportions of the.

Repeated experiments were made in predetermining

the relation between its height and width.

But every attempt

to do so was finally discarded in the interest of making the picture’s proportions subservient to what the picture had to say. Discoveries resulting from failure. Up to this point the mathematical approach to design had, in the particular case here discussed, proved worse than useless. ever, had been gained from experiment.

Much, how­

Negatively, the

student's long-standing distrust of so-called “dynamic

31 symmetry" now had an objective basis.

It would seem that

any theory of design which predetermines not only a picture’s height-width ratio but its main divisions were better called "static symmetry".

Positively, on the other hand, the value

of a geometric foundation to the work of the Italian Renais­ sance painters became evident.

Much of the composition of

that period being bilaterally symmetrical, such a geometric pattern provided an effective means of correlating the design with the perspective scheme, which characteristically employed a single vanishing point. f, This particular compo­ sition, however, involved three vanishing points, all outside the picture, and was the product of a period which regarded bilateral symmetry in composition as dull. Two new points of departure.

Two fresh lines of specu­

lation now developed: 1.

In the course of twenty-odd years the student had

heard repeatedly, from a variety of persons, the observation that the antique Greek vases, on which Jay Hambidge and others labored so earnestly to prove that their proportions had been determined

geometrically, were probably the

product entirely of experienced taste and a discriminating

6 A geometric plan also aided in harmonizing the painting with surrounding architecture, as in fresco work.

32 eye, that a geometric aspect could be demonstrated in any highly satisfactory work of paintings sculpture, or archi­ tecture, but that this was an unconscious result stemming from the very nature of human taste.

If such were the case,

it would be interesting to carry the composition to as ad­ vanced and satisfactory a state as possible, and then to analyse it, on the possibility that such a geometric aspect could be discovered in those divisions of the picture plane which had been fixed upon merely because they seemed most satisfying. 2.

It has already been remarked that In the first

stage of developing the composition a study had been made of the porch as a problem In three-point perspective, but that in the second stage this study had been merely a point of departure, the elements of the porch being moved this way and that to contribute to the structure of the composition. The question arose, had the geometric forms of the porch, In the course of the rearrangement, been brought Into har­ mony with some other, and determinable, set of laws, than those of linear perspective? These speculations were laid completely aside until the composition had reached the state shown in Illustration 18.

They were then resumed, a somewhat satisfactory conclusion

33 to both being unexpectedly found at one time. Second and more successful application. A tracing was made of the oil study reproduced in Illustration 18.

The

margins were divided in mean proportion, these divisions were in turn divided in the same manner, and these latter again.

The midpoints of the sides were also taken.

The

basis, inspiration, or point of departure, for this division was the "harmonic analysis" of the rectangle.7

Departures

from these were two-fold; first, the ratio between the rect­ angle's sides was not predetermined geometrically, but had grown out of the demands of the composition as a threedimensional study; second, a symmetrical grid of intersecting lines (a ghost of the Renaissance, it seemed to the student) was not laid down with the idea of discovering how the com­ position could be fitted into it. Rather a series of ten­ tative experiments were made, with no idea of bilaterial symmetry in mind, to see which If any lines, vertical, horizontal, or diagonal, connecting the divisions of the edges, were in agreement with the significant features of the composition.

The experiments continued on several

superimposed sheets of tracing paper.

7 See Ghyka, op. cit., pp. 31 and 166 .

3^ Results derived from application. The results were somewhat satisfactory.

Not only did the most important

divisions in the composition occur along or near lines connecting important division points on the edges, but wherever the composition was altered to coincide with or approach such lines, an improvement was usually noticeable. More than this, a number of "subjective" lines which had gone either unnoticed or insufficiently exploited, were brought to the student1s attention. A schematized version of the composition, based on Illustration 18, but incorporating the improvements developed in the experiment, was now made, the light and dark being again simplified to four shades.

The result is shown in

Illustration 19. A weakness was thus exposed and pointed out by the advisor, namely a crowding of the ascending figure against the right side of the rectangle, and a slight lack of space in the foreground (illustration 19 was photographed after these corrections in area had been made.). With these area changes the ratio between height and width finally became fixed at eleven to six. The correction, altering as it did the position of all mean-proportional divisions and midpoints on the edges, occasioned a complete reworking, even though a slight one,

36

of the geometrical aspect of the design scheme.

The re­

working* before being undertaken* occasioned nothing but trepidation.

Surprisingly the whole composition seemed

slightly to improve under it* and additional parts now fell into place.

The result of this reworking is shown

in Illustration 20.

For a simplified linear version of

it* indicating (for clarity’s sake on so small a scale) only some of the important geometric lines on which it is constructed* see Illustration 21.

Midpoints of sides are

indicated by M* mean proportional divisions of the whole dides by

* subdivisions of these by 4> 2 (subdivisions in

turn of these* marked ^ 3 * were very little used.). Attention is called to the following features: 1. The most interesting parts of the picture (including the women’s heads) both fall on important Intersections. 2. Every important form or line of direction in the composition can be shown to lie along one or another of the geometric lines dividing the rectangle. 3. While the lines of the porch are approximated to those of linear perspective* they now actually coincide with* or are parallel to* lines determined by the geometrical di­ visions of the sides of the canvas* and thus are brought into harmony with laws determined by the limiting rectangle itself.

37 4.

The figures of the women may be said to lie within

a series of intersecting pyramids, whose apices lie on the boundary of the rectangle, and whose edges touch or lie along, salient features in the figures. Advantages of geometric approach to this composition1s pattern. In conclusion, the student found a geometric approach to design of value to this particular composition in the following ways: 1. It aided a final adjustment of the parts of the composition. 2. It provided a fresh angle of approach, a "fresh eye" to the work in an advanced stage, when most needed (witness the discovery of the need for area change). 3. It aided the discovery and strengthening of "sub­ jective" lines which might otherwise have been overlooked. That there is a connection between taste in design, and geometry, was perhaps indicated.

The possibility that

such a connection, if it exists, might be more fully uti­ lized with additional experience was also perhaps Indicated. That the use of such a geometric approach is no safe­ guard against uninteresting or cluttered composition can be demonstrated by various concrete examples, notably some of the illustrations in Hambidge1s "Dynamic Symmetry in Composition",

38 and. by some of George Bellows1 painting after he had become a devotee of dynamic symmetry.

See, for example, the back­

ground of the figures in his “Two Women11. The purpose of the blocked version of the composition (illustrations 19 and 20) was solely that of the other ab­ stractions which had been made during its growth, namely to serve as a point of departure for continued development, not as a rigid limitation upon it.

The pointlessness of adhering

too closely, even to lins and divisions as carefully placed as those in 19 and 20, is best illustrated by an observation of William Hogarth’s taken slightly but harmlessly out of context: It may be observed, that minute differences of great lengths, are of little or no consequence as to proportion, because they are not to be discerned; for a man is half an inch shorter when he goes to bed at night, than when he rises in the morning, without the possibility of its being perceived.° Conclusion.

The composition now might be said to have

not only a spatial organization and a satisfactory distribu­ tion of light and shadow, but an acceptable two-dimensional pattern as well.

To achieve this certain distortions had

been made in the forms.

These will be discussed next.

Afterwards the composition will be considered as a color problem.

® William Hogarth, The Analysis of Beauty, Chapter XI ^

39

I l f 14

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CHAPTER VI

THE COMPOSITION AS AIDED BY DISTORTION Mention has already been made of the departure from linear perspective in the drawing of the porch.

This depar­

ture was of two kinds, which might be described, respectively, as modifications and violations. As modifications may be classed the lines of the porch which seem to converge in a vanishing point to the right, but which actually do not, their direction being determined by geometrical divisions of the rectangle’s edges. As violations may be classed the left-hand edges of the porch steps, which do not appear to converge even slightly in a vanishing point, their purpose being to lead the eye down from the left-hand post and around to the right foot of the ascending woman. So far as the women themselves are concerned, there is here also a distortion, observable particularly from a com­ parison of the final life study for the ascending women (Illus­ tration 9) and the form the figure had taken by Illustrations 18, 19 3 and 20.

The lower part of the body, in the interests

of carrying the eye up and. giving lightness, Is drawn as if seen from an eye level near the woman’s shoulders.

On the

42

other hand, the ellipse formed by the embracing arms of the women is tipped as if seen from a position well above the women's heads,, the purpose here being to carry the eye of the observer, at first strongly up and leftward along the descending woman's arm, then up and rightward along her shoulder line. These various distortions were experimented with at some length, in the course of which they were carried to extremes eventually discarded.

CHAPTER VII

THE COMPOSITION AS COLOR AND AS AIDED BY MANNER OP TREATMENT Color sketch. After some experiment, a color sketch was prepared as follows:

A light-and-dark study like Illus­

tration 20 was made in warm browns on a small scale . After it was dry, contrasting cools were introduced on it in grey, and then, little by little, the colors.

For this procedure

the student was chiefly indebted to the advisor. Choice of palette. Since previous studies (and it seemed to him some other of his painting) had leaned over-heavily on blue, the student decided, for experience' sake, to try elimi­ nating blues entirely, and, the better to hold the color scheme together, to work with a fairly limited palette.

Ex­

periment finally reduced this palette to cadmium red deep, Venetian red, burnt Siena, cadmium yellow medium, and viridiam, besides ivory black and silver white. Distribution of warm and cool tones.

The general plan

of warm and cool was developed, In Its broadest terms, as follows:

The warmest tones to be on the foremost figure,

and to become progressively cooler in the figure group, culminating In the frosty white of the descending woman's

44 hair.

Other warm-cool contrasts to he much less pronounced:

The hard-pounded earth in the foreground to be neutral, the facing of the porch to be warm-neutral, the surface of steps and porch- floor to be colder, the wall of the house to be neutral again, etc. In working on the color the student was continually faced with the fact that the kind of place whose mood the composition was intended to capture has, in his experience, a meager poverty of tone, almost amounting to deadness, with which the dress of the older people is generally in agreement, and that of younger persons often in violent contrast.

He

found himself thinking of the two women as being on opposite sides of this "color line", and since the resulting problem of somehow weaving richness and poverty of color into a har­ monious whole was a challenging one, he did not resist it. The question of local authenticity was not his prime concern, especially since life in this country tends to rub off the characteristics and dull the colors which foreigners bring with them.

It seemed more important that the observer

share to some degree the solemnity and high emotion with which two women, acquainted with poverty and hard work, might meet after long separation.

^5 First manner of painting final canvas, and why unsatisfactory.

The final canvas, fifty-five inches high, now being

ready, an exact enlargement of Illustration 20, in line only, was traced upon it.

All the darkest areas were then painted

in, the degree of darkness being determined from Illustration 19, the color from the color sketch.

This process was re­

peated in turn for the other three degrees of dark-and-light. The question then arose whether such a mode of treatment might not be satisfactory as a final painting. When the canvas was covered, the advisor considered it an underpainting and no more.

The areas fell apart, in­

stead of holding together as do those in the dark-and-light studies.

The colors, carefully mixed to the right shade and

hue before application, had the flat, milky quality of house paint, devoid of the variation and sparkle which are the life of oil painting.

Moreover, there was something about this

hard, analytical method, utterly devoid of texture, which was incompatible with a subject so charged with sentiment. The student therefore returned to his original inten­ tion of using Illustration 20 as a point of departure only. The canvas was reworked boldly and freely, In what might be called a chiaroscuro manner. and rough.

The painting was rather broad

Varieties of texture were treated as sympathetically

as the student’s powers permitted.

Departures were made from

46

the original precise forms wherever the spirit of the picture, or the subject treated, seemed to call for it.

The fact that

these departures were all so slight as not to violate the structure of the painting as determined in Illustrations 20 and 21 was the result of this structure’s seeming to be satis­ factory, not of caution. The study of hands (illustration 12) was freely drawn upon for the first time, as was the sketch for the descending woman’s head (Illustration 22). When the canvas reached a point of development beyond which there seemed to be the risk of overworking, it was sub­ mitted to the advisor and after some additional helpful changes made on his advice, was approved by him.

The final state of

the canvas is shown in Illustration 23. Conclusion.

The advisor’s opinion of the finished

painting was that as a study of forms in space, and light and shade, it was fairly adequate, and satisfactorily placed on the canvas.

In color, however, it was considered uneven,

the upper part of the porch being uninteresting in its color relations, and thus inconsistent with other parts of the painting.

41

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BIBLIOGRAPHY Some of the books listed below are too well known, or too accessible, to need comment.

Where neither of these

seems the case, a descriptive sentence or cursory evaluation has been added. Allston, Washington, Lectures on Art, and Poems. Baker and Scribner^ TB50T

New York:

The third lecture, On Composition, is a rewarding investigation of the subject. The second lecture contains a valuable discussion (the best the student has yet found) of the uses and abuses of systems of human proportion. Dali, Salvador, Fifty Secrets of Magic Craftsmanship. York: Dial Press, 1948.

New

The discussion of the use of the mean proportion in composition takes a different direction from that in this thesis, but does not conflict with it. Doerner, Max, The Materials of the Artist and Their Use in Painting. Eugene Neuhaus, translator; New York: Harcourt Brace, 19^9D$rer, Albrecht, Underweysung der Messung mit dem Zirckel und Richtscheid. Ndrenberg: Formenschneider, 153&. ______ , Vier Buecher von Menschlicher Proportion. Formenschneider, 1528.

N#renberg:

The chief value of these works turned out to be a revelation of D$rer1s mathematical erudition, his refreshing inventiveness in conveying it clearly, and his endless patience in pursuing problems, particularly the search for a statistical basis of human proportion.

50 Francesca,, Piero della, De Prospectiva Pingendi. Manuscript composed sometime be tween 1470 and 1490. The following printed versions were used here: 1. Edizione Critica a Cura di G. Nicco Fasolo.

Firenze,

IcpPZZ 2. Nach dem Codex der Kffniglichen Bibliothek zu Parma nebst Deutscher Ubersetzung zum ersten male Ver8ffentlicht von D r . C. Winterberg, Strassburg, 1899. The former is preferable for its photographic reproduc­ tions of the beautiful pen diagrams of the original manuscript; the latter for the analyses of several of Piero's compositions, in the introduction. Ghyka, Matila, The Geometry of Art and Life. New York: Sheed and Ward, 1946. The best and briefest summary the student has yet found of the various sides of this subject. Greenough, Horatio, A Memorial of Horatio Greenough. Twelve of Greenough's essays edited by Henry T. Tuckerman; New York: 1853. Contains some eloquent crusading for functionalism in the arts; a book ahead of its time. Hambidge, Jay, Dynamic Symmetry in Composition as Used by the Artists. New York: Coward McCann, 1923Hogarth, William, The Analysis of Beauty. Written with a view to fixing the fluctuating Ideas of Taste. London: J. Reeves, 1753Value chiefly historical. The discussion of the impracticability of systems of human proportion is a useful one, but surpassed, it seemed to the student, by Allston’s. Klee, Paul, The Pedagogical Sketch Book. Sibyl Peech, trans­ lator; New York: Nierendorf Gallery, 1944. Loran, Erie, Cezanne's Compositions. Berkeley: of California Press’! 19465

University

51 Maroger, Jacques, The Secret Formulas and Techniques of the Masters. New York: Studio Publications, 1948. Missel, Ernst, Vom Geheimnis der Form and der Urform des Seins. Stuttgart: Deutsche Verlags-Anstalt, 1938. A history of the uses of mathematics in composition; full of simple and lucid diagrams. A fascinating book. Nicholls, Bertram: Painting in Oils. New York: Publications, 1948.

Studio

Pacioli, Luca: Divina Proportione Opera